lean_workbook_plus_67157

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove the Cauchy inequality using the hardest way possible.\nCauchy inequality:\n\n

(a^2+b^2)(c^2+d^2) \geq (ac+bd)^2

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_67157 (a b c d : ℝ) :
  (a^2+b^2)*(c^2+d^2) ≥ (a*c+b*d)^2   :=  by sorry

Source